The classical “butterfly” graph is the
doubly-odd paddle graph of order 5. All doubly-odd paddle graphs of the same
order \(p\)  have isomorphic normal algebras \(\mathcal {T}_{p}\) . The number of
such graphs is the number of pairs \(\left\lbrace  m,n\right\rbrace  \)  of odd integers \(n,m\ge 3\)  with \(n+m\le p+1\) , \(n=m\)  allowed. The sequence of counts,
starting at \(p=5\) , is presented in [1]}. (The number
of unrestricted paddle graphs is also there [1]}.)
